The invention relates to a tuning apparatus and method, and more particularly, to an apparatus for tuning a center frequency of a filter and related method thereof.
Filters have been widely used in many applications. In general, the implementations of the filters can be roughly divided into two types of structures, which are discrete-time switch-capacitor filters and continuous-time filters (including gm-C filter, MOSFET-C filter, etc.). Because of the limitation of clock frequency, a high-frequency filter is often implemented by the continuous-time structure. Furthermore, in different types of continuous-time filters, the gm-C filter is the most general.
However, the variation degree of some characteristics, such as cut-off frequency (center frequency), of the continuous-time filter is often larger than 30% due to the influences of variations in the manufacturing process and temperature variations. Therefore, a tuning mechanism should be added into the filter to overcome the process and temperature variations such that the frequency response of the filter is not affected by the influences of the process and temperature variations.
In the gm-C filter structure, the cut-off frequency (center frequency) can be represented by the following equation wc=K*gm,u/C, where gm,u represents a gm (trans-conductance) value of a trans-conductor per unit, C represents a total capacitance value corresponding to a node, and K is a scaling factor larger than 0. From the above equation, it can be seen that when the center frequency wc deviates from a target value, the gm value gm,u or the capacitance value C can be adjusted to tune the center frequency wc back to the target value. In order to achieve the purpose of tuning the center frequency wc, either the gm value gm,u or the capacitance value C can be adjusted. Please note that adjusting the gm value gm,u or the capacitance value C is equivalent. The spirit of the two adjusting methods is the same.
Taking the method of adjusting the gm value gm,u as an example, please refer to FIG. 1, which shows a conventional tuning structure 100 of adjusting the gm value gm,u of a main filter 110. Please note, the main filter 110 is a target filter to be tuned. Furthermore, in FIG. 1, the tuning operation is performed by a PLL (including FD 120 the charge pump 121 and the loop filter 122) cooperating with a VCO 130. Please note, under the tuning structure 110 shown in FIG. 1, the VCO 130 is better composed of the same trans-conductor cells as those of the main filter 110, the VCO 130 has the same environment (e.g., loading, etc.) as the main filter 110, and the gm value of the trans-conductor circuits of the VCO 130 and the main filter 110 are controlled by the same control signal Vc. Therefore, if the tracking relationship between the VCO 130 and the main filter 110 is better, the tuning operation of the tuning structure can be more accurate. In other words, when the VCO 130 is tuned, the main filter 110 is also tuned because they have similar environment. Assume that the center frequency wc of the main filter 110 is ideally equal to the K*gm,u/C, and the oscillation frequency wo of the VCO 130 is equal to N*gm,u/C. When the PD 120 of the PLL is locked to a certain frequency, the control signal Vc is adjusted to change the gm value gm,u such that the fo=(1/2π) (N*gm,u/C)=fref. As mentioned previously, the main filter 110 and the VCO 130 has a good tracking relationship (e.g., they have the same gm value gm,u). Therefore, fc=(1/2π) (K*gm,u/C)=(K/N)fo=(K/N)fref. Obviously, if the values K, N, and fref can be selected properly, the center frequency of the main filter 110 can be tuned to a target frequency.
Please refer to FIG. 2, which is a diagram of another conventional tuning structure 200. Please note, the tuning structure 200 shown in FIG. 2 utilizes a similar concept. The tuning structure 200 utilizes similar trans-conductor cells to form the master filter 230 (in general, the master filter shown in FIG. 2 has lower levels), and utilizes the characteristic of the master filter 230 to perform the tuning tasks. For example, a two-level Biquad LPF has a 90 degree phase delay at the point where wo=N*gm,u/C. Therefore, when the signal having the frequency fref is inputted into the master filter 230, the entire tuning structure 200 utilizes the phase detector (PD) 220 to determine whether the phase difference is 90 degrees. Additionally, recall as mentioned previously, the feedback mechanism is implemented by a PLL including a charge pump 221 and a loop filter 222, the negative feedback mechanism adjusts the control signal Vc to make the fo=(1/2π) (N*gm,u/C)=fref. From the above-mentioned structure, it can be easily seen that fc=(1/2π) (K*gm,u/C)=(K/N) fo=(K/N) fref. Therefore, the tuning structure 200 shown in FIG. 2 can also achieve the same tuning goal.
The above-mentioned structures both needs a PLL including a PD, a charge pump, and a loop filter. It is known that the PLL occupies a larger area and as one result, this increases the cost. Please refer to FIG. 3, which is a diagram of another conventional tuning mechanism 300. The tuning mechanism 300 utilizes a digital circuit 320 to perform a negative feedback control. The entire tuning method shown in FIG. 3 is more similar to the tuning structure shown in FIG. 1. The difference between the tuning structures shown in FIG. 3 and FIG. 1 is that the tuning structure shown in FIG. 3 utilizes a digital circuit 320 (i.e., a digital FD) to compare the frequency fref with the frequency fc generated by the VCO 330 instead of utilizing a PLL. Thereby, the comparison result is transformed into a control signal through a DAC 340 in order to adjust the frequency fc. Similarly, because of the tracking relationship between the VCO 330 and the main filter, when the oscillation signal of the VCO 330 is tuned, the cut-off frequency of the main filter 310 can be tuned successfully.
The influences caused by the process and temperature variations upon the frequency fc, can be alleviated through the above-mentioned tuning mechanisms. Obviously, the above-mentioned tuning mechanisms need either a VCO or a master filter. Furthermore, either the VCO or the master filter is often a two-level system. In addition, in order to make the environment similar to the main filter, all dummy devices, dummy loading, and other circuits, which have originally been set up in the main filter, also have to be copied and implemented inside the tuning structure (e.g., the above-mentioned VCO or master filter) to make the environment similar. In most of the applications, the tuning structure often occupies a huge area larger than 20% of the entire circuit. Therefore, the above-mentioned tuning mechanism consumes a large area and high cost resulting in an uneconomical solution.